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A simple structural estimator of disclosure costs


This study recovers a simple firm-level measure of disclosure costs implied by the voluntary disclosure theory of Verrecchia (Journal of Accounting and Economics 12(4), 365–380, 1990). The measure does not require knowledge by the researcher of the distribution of private information and can be implemented with three simple observable inputs: the minimum, average, and frequency of disclosure. We document a positive association of disclosure costs with proxies for existing and potential competition, information asymmetry, and insider trading. Higher values of disclosure costs are associated with lower contemporaneous and future disclosures as well as lower propensity to disclose in holdout samples. Overall, we provide future researchers with an easy-to-implement procedure to structurally estimate unobserved firm-level disclosure costs.

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Fig. 1


  1. Following Verrecchia (1990), we have left aside considerations of risk-aversion modeled in the original Verrecchia (1983) model; that is, we assume that the set of potential investors is large, and the disclosure is about a diversifiable component such that there is risk-neutral pricing of the disclosed value (Cheynel 2013). For a more comprehensive empirical analysis of settings with a small investor base, see Armstrong et al. (2011). Note that investor risk-aversion increases the willingness to disclose for a given cost, since markets discount more risky non-disclosure. Therefore risk-aversion would directionally predict higher disclosure costs than those under risk-neutrality.

  2. In other words, if the market price is \(P(\mathcal {I})= \alpha \mathbb {E}(e|\mathcal {I})\), estimated variables can be rescaled by α, which can be estimated empirically. We omit α since it plays no further role in the estimation.

  3. Within product market theories, information may be proprietary, and thus c is positive because disclosure will benefit existing competitors (e.g., Verrecchia 1983; Dye 1986). At the same time, depending on the effect of disclosure on the aggressiveness of potential competitors, disclosure can entail some benefits (e.g., Darrough and Stoughton 1990). Disclosure may mitigate agency costs stemming from diverging interests between owners and managers and affect investment efficiency (e.g., Stocken and Verrecchia 2004; Liang and Wen 2007). Or disclosure may reduce the risk of a shareholder lawsuit (e.g., Skinner 1994; Skinner 1997) or reduce information asymmetry (e.g., Diamond and Verrecchia 1991). Other disclosure costs can take the form of processing, communicating and producing the information to outsiders as well as psychological costs and reputational concerns. The cost c is positive in aggregate.

  4. The model is laid out as if the manager paid the cost directly, mainly to avoid having to redefine the price equation to include the costs and burdening the exposition.

  5. Our cost estimation approach still works even if there are multiple equilibria as long as the same equilibrium is implemented during the sample period. More assumptions are typically needed to guarantee the existence of a unique equilibrium. For example, if x is logconcave with sub-exponential lower tail, there exists a unique interior equilibrium. The proof of uniqueness follows immediately from the definition of logconcavity. Without sub-exponential lower-tail, there may be equilibria featuring unravelling even if the cost is non-zero (e.g., Laplace distributions); we refer to Bertomeu and Cheynel (2018) for a proof of a unique interior equilibrium as long as the lower tail becomes small at a rate greater than exponential rate. As a special case, this is always true if the distribution is bounded from below. Note that, strictly speaking, we can lift the requirement of logconcavity and sub-exponential tail as long as we assume that the entire sample is generated from players coordinating on one interior equilibrium.

  6. The validity of your approach is contingent upon the equilibrium being characterized by a threshold and some relations between the cost and x could undermine that equilibrium characterization.

  7. We can approximate \(\mathbb {E}(x|x\leq \tau )\) by computing the average earnings surprise for firm quarters for which there is no disclosure in the data, but this estimation procedure entails many caveats. First, it assumes that the private information is formulated in terms of posterior expectations, such that \(\mathbb {E}(e|ND)=\mathbb {E}(x|ND)\) by the law of iterated expectations. Second, empirically, because we do not know when the manager receives his information, we cannot measure accurately the consensus and need to make choices when to pick the consensus, which is likely to add noise in the estimation. The estimation procedure that we adopt is not sensitive to these choices. We express \(\mathbb {E}(x|ND)=-\frac {p}{1-p}\mathbb {E}(x|x>\tau )\) such that both p and \(\mathbb {E}(x|x>\tau )\) can be measured directly in the data.

  8. In Appendix A, we derive the asymptotic variance of the BBT and NP estimators.

  9. While our empirical analyses will focus on the NP estimator, we show in Appendix B that the model can serve as a starting point for richer settings; we also discuss how to modify (or sometimes reinterpret) the analysis in three plausible alternative settings. Specifically, our NP estimator derived under pure disclosure costs continues to hold after including other disclosure frictions. For example, it is robust to a probability that the manager does not receive private information or to a probability that the manager receives some information that she would like to disclose, but she cannot convey it credibly, as in Dye (1985). It can also incorporate an exogenous probability that forces the firm to disclose or a probability that the manager does not care about maximizing the price and never discloses.

  10. Everything else held equal, a greater frequency \(\hat {p}\) implies a higher proprietary cost. This last property is seemingly counterintuitive, that is, one might expect a firm that discloses more often to have low proprietary costs. To see why this occurs, consider the case when c is small; then \(\hat {p}/(1-\hat {p})\) becomes large but, at the same time, the average forecast surprise \(\mathbb {E}(x|x>\tau )\rightarrow \mathbb {E}(x)=0\). The two effects offset each other; a high forecast frequency, controlling for the forecast surprise, tends to indicate a higher cost. The frequency effect on the NP-cost estimator stands in contrast to the effect on the BBT estimator. This observation illustrates that a negative correlation between the NP-cost estimator and disclosure is not by construction but will hold under the assumptions of the theoretical model.

  11. Einhorn (2007) develops a more general voluntary disclosure model, where the manager might either maximize or minimize the price at a cost if he decides to disclose. In equilibrium, low and high outcomes are disclosed, and intermediate earnings are never disclosed. However, this intermediate non-disclosure region does not appear to be consistent with the observed management forecasts.

  12. The cost here is a personal cost, in line with the presentation used in the main analysis. The manager solely minimizes the perception of the price similarly to Einhorn (2007). However, we could also assume that the manager minimizes the total cash flows, i.e., subtracting the cost from price via a decrease in future earnings, and this alternative formulation would result in minor changes.

  13. Note that this effect is not driven by small-sample deviations from asymptotic theory, as the asymptotic standard-error of the estimator increases when trying to estimate small costs as shown in Appendix A.

  14. We select this period for two reasons. First, the implementation of Regulation Fair Disclosure (Reg. FD) in the United States closed private channels of communication to analysts and thus greatly increased the number of forecasting firms for reasons unrelated to disclosure costs. Second, in previous years, management forecasts were not systematically collected by the First Call Company Issued Guidance (CIG) database, but after 2003, the requirement by Sarbanes-Oxley to record transcripts of conference calls greatly improved forecast archives. Prior to 2003, many forecasts were made during unrecorded conference calls, thus leading to systematic omitted forecast data for smaller firms that are less likely to trigger follow-up press releases.

  15. Because management forecasts of EPS are typically adjusted, we use the ratio of unadjusted to adjusted EPS to convert these forecasts to raw forecasts. Adjusted forecasts are problematic because, for firms that had stock splits, the variance of adjusted forecasts will decline over time. In cases of zero adjusted EPS (which can occur because earnings are zero or because of two-digit rounding given very large splits), we use the nearest available adjustment factor, thereby dropping observations that have no adjustment factor.

  16. Since CIG reports adjusted EPS forecasts, we recover unadjusted forecasts using the adjustment factor, i.e., the ratio of unadjusted to adjusted EPS, to convert these forecasts to raw forecasts.

  17. We can make no theoretical predictions about the correct variable to measure and scale surprises. For example, in the context of management earnings forecasts, one might use any variable capturing market change in expectations, such as short-window market response (Kasznik and Lev 1995), earnings per share (Cheong and Thomas 2011), or earnings surprise scaled by lagged assets or prices.

  18. Li (2010) classifies MKTS into two categories as a measure of existing competition as well as potential rivals. Firms generating high sales may operate in environments where the number of existing rivals is larger, and they may avoid disclosing information that competitors might use to their advantage.

  19. We define high litigation industries as those with SIC code 2833-2836, 8731-8734 (biotech), 3570-3577 (computer hardware), 3600-3674 (electronics), 7371-7379 (computer software), 5200-5961 (retail), 4812-4813, 4833, 4841, 4899 (communications), or 4911, 4922-4924, 4931, 4941 (utilities), as defined by Ajinkya et al. (2005).

  20. While we conduct our analysis using both logit and OLS regressions, we tabulate the OLS regressions, because these are less sensitive to the inclusion of fixed effects compared to logit and with marginal effects that are simpler to interpret (Angrist and Pischke 2008).

  21. Our results are qualitatively similar if the holdout period consists only of the firm-quarters in 2016.

  22. The four-digit Standard Industrial Classification (SIC) codes used by government agencies to classify industry areas remain quite popular, but this is being supplemented by the six-digit North American Industry Classification System (NAICS) codes. The Global Industry Classifications Standard (GICS) system that has been jointly developed by Standard & Poor’s and Morgan Stanley Capital International (MSCI) is popular among financial practitioners, whereas the 48 Fama and French classification tends to be more popular in academic research.

  23. Not all of the 48 industries are tabulated because some of them did not contain the minimum requirement of five firms.

  24. In untabulated results, we examine the correlations between \(\hat {c}_{NPALT}\) and the competition variables. This measure \(\hat {c}_{NPALT}\) correlates with proxies capturing competition from potential rivals, with the exception of R&D. The evidence is more mixed with measures of existing competition. The alternative measure correlates positively with the HHI variable, whereas the correlation with NUM is insignificant. Lastly, the correlation is negative with CAPX, consistent with the existence of barriers to entry.

  25. Federal laws govern insider trading in the United States, and several pieces of legislation concerning insider trading include the following: the Securities Act of 1933, the Securities and Exchange Act of 1934, and the Sarbanes-Oxley Act of 2002. On August 10, 2000, the Securities and Exchange Commission (SEC) adopted Rules 10b5-1 and 10b5-2 that clarify certain principles of insider trading while simultaneously announcing the adoption of Regulation FD (Fair Disclosure), which prohibits public companies from selectively disclosing information.

  26. In untabulated tests, we also include lagged insider trading to control for unobservable factors that affect insider trading. The results are qualitatively similar.

  27. In fact, this equation is exactly the same as in Jung and Kwon (1988), subtracting the cost from the disclosing firm price, i.e., changing τ into τc.


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We warmly thank Jeremy Bertomeu, Moritz Hieman, Hui Chen, Ivan Marinovic, Korok Ray, Paul Fischer, Michael Kirschenheiter, and participants at the Stanford Summer Camp (2015), the Burton Workshop at Columbia Business School (2015), the Annual American Accounting Association (2016), the Rady School of Management Workshop (2016), and the tenth Accounting Research Workshop at Basel (2017) for helpful feedback.

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Appendix: A

1.1 Asymptotic properties of the estimators

We derive the asymptotic properties of the BBT-cost and NP-cost estimators.

Proposition 1

If c > 0, the estimator cBBT is consistent (\(plim \hat {c}_{BBT}=c\)) with asymptotic variance given by

$$ \sqrt{N}(\hat{c}_{BBT}-c)\rightarrow_{d} N(0,\sigma_{BBT}^{2}), $$

where \(\sigma _{BBT}^{2}=(H^{\prime }(p))^{2}p (1-p)\) and \(H^{\prime }(p)=-\frac {1}{\phi ({\Phi }^{-1}(1-p))}-\frac {\phi ^{\prime }({\Phi }^{-1}(1-p))}{(1-p)(\phi ({\Phi }^{-1}(1-p)))}+\frac {\phi ({\Phi }^{-1}(1-p))}{(1-p)^{2}}\).

Likewise, cNP is consistent (satisfies \(plim \hat {c}_{NP}=c\)) with asymptotic variance given by

$$ \sqrt{N}(\hat{c}_{NP}-c)\rightarrow_{d} N(0,\sigma_{NP}^{2}), $$

where \(\sigma _{NP}^{2}= \frac {p (p m + m (1 - p))^{2} + (1 - p) p v_{x}} {(1 - p)^{3}}\) and \(v_{x}=Var(\tilde {x}|\tilde {x}\geq \tau )\).

The asymptotic variances of the estimators \(\hat {c}_{BBT}\) and \(\hat {c}_{NP}\) can be easily estimated using sample moments, that is, replacing all elements of the asymptotic variance by their sample estimates, i.e.,

$$ \begin{array}{@{}rcl@{}} \hat{\sigma}_{BBT}^{2}&=&(H^{\prime}(\hat{p}))^{2}\hat{p} (1-\hat{p}),\\ {and} \hat{\sigma}_{NP}^{2}&=& \frac {\hat{p} (\hat{p} \hat{m} + \hat{m} (1 - \hat{p}))^{2} + (1 - \hat{p}) \hat{p} \hat{v}_{x}} {(1 - \hat{p})^{3}}, \end{array} $$

where \(\hat {v}_{x}\) is the sample variance of forecasts, then \(\hat {\sigma }^{2}_{BBT}\) and \(\hat {\sigma }^{2}_{NP}\) are respectively consistent estimators of \(\sigma ^{2}_{BBT}\) and \(\sigma _{NP}^{2}\).

Proof of Proposition 1:

The proof of consistency is immediate. By continuity, the estimator \(\hat {c}_{BBT}\) is consistent. Likewise, by continuity, the estimator \(\hat {c}_{NP}\) is consistent, satisfying

$$ plim \hat{c}_{NP}=plim\hat{\tau}+\frac{plim\hat{p}}{1-plim\hat{p}}plim\hat{m}=\tau+\frac{p_{}}{1-p}\mathbb{E}(x|x\geq \tau)=c^{}. $$

Let us derive the asymptotic variances next.

$$ \begin{array}{@{}rcl@{}} \sqrt{N}(\hat{p}-p)\rightarrow_{d} N(0,p(1-p)) \end{array} $$

Applying the Delta method,

$$ \sqrt{N}(\hat{c}_{BBT}-c)\rightarrow_{d} N(0,(H^{\prime}(p))^{2}p (1-p) ), $$

where \(H(p)={\Phi }^{-1}(1-p)+\frac {\phi ({\Phi }^{-1}(1-p))}{1-p}\). Taking the derivative of H(p) completes the proof.

We denote xi as the manager’s information and di as the disclosure for each observation i, where di = 1 if a forecast is issued or di = 0 otherwise.

$$ \hat{c}_{NP}=\hat{\tau}+\frac{\hat{p}}{1-\hat{p}}\hat{m}=\hat{\tau}+\frac{\sum d_{i}/N}{1-\hat{p}}\frac{\sum d_{i} x_{i}}{\sum d_{i}}=\hat{\tau}+\frac{1}{1-\hat{p}}\underbrace{\frac{\sum d_{i} x_{i}}{N}}_{\hat{w}}. $$

In what follows, let us denote \(\tilde {x}\) as the random variable, corresponding to the manager’s private information, and \(\tilde {d}=1\) if a forecast is issued or d = 0 otherwise. The associated moments to these random variables are denoted \(m= \mathbb {E}(\tilde {x}|\tilde {x}\geq \tau )\), \(v_{x}= Var(\tilde {x}|\tilde {x}\geq \tau ),\) and \(\mathbb {E}(\tilde {d}\tilde {x})=p \mathbb {E}(\tilde {x})=pm\). Note that \(\hat {p}\) and \(\hat {w}\) are sample means. Therefore, by the central limit theorem,

$$ \sqrt{N}\left( \left( \begin{array}{l} \hat{p} \\ \hat{w} \end{array}\right)-\left( \begin{array}{l} p \\pm \end{array}\right)\right) \rightarrow_{d} N(\mathbf{0}_{2},\underbrace{\left( \begin{array}{ll} Var(\tilde{d}) & cov(\tilde{d},\tilde{d}\tilde{x}) \\ cov(\tilde{d},\tilde{d}\tilde{x}) & Var(\tilde{d}\tilde{x}) \end{array}\right)}_{{\mathbf{V}}_{\mathbf{0}}}. $$

Simplifying this variance-covariance matrix and denoting \(m= \mathbb {E}(\tilde {x}|\tilde {x}\geq \tau )\) and \(v_{x}= Var(\tilde {x}|\tilde {x}\geq \tau )\),

$$ {\mathbf{V}_{\mathbf{0}}}=\left( \begin{array}{ll} p(1-p) & (1-p)p m \\ (1-p)p m & p(v_{x }+(1-p)m^{2}) \end{array}\right) $$
$$ \begin{array}{@{}rcl@{}} \text{because} Var(\tilde{d})&=& p(1-p);\\ cov(\tilde{d},\tilde{d}\tilde{x})&=& \mathbb{E}(\tilde{d}^{2}\tilde{x})- \mathbb{E}(\tilde{d})\mathbb{E}(\tilde{d}\tilde{x})\\ &=& \mathbb{E}(\tilde{d}\tilde{x})- \mathbb{E}(\tilde{d})\mathbb{E}(\tilde{d}\tilde{x})=(1-p)\mathbb{E}(\tilde{d}\tilde{x})\\ &=& (1-p)p \mathbb{E}(\tilde{x}|\tilde{x}\geq \tau)=(1-p)p m; \end{array} $$
$$ \begin{array}{@{}rcl@{}} \text{and} Var(\tilde{d}\tilde{x})&=& \mathbb{E}(\tilde{d}^{2}(\tilde{x})^{2})- \mathbb{E}(\tilde{d}\tilde{x})^{2}\\ &=& \mathbb{E}(\tilde{d}(\tilde{x})^{2})-(p \mathbb{E}(\tilde{x}|\tilde{x}\geq \tau))^{2}\\ &=& p \mathbb{E}((\tilde{x})^{2}|\tilde{x}\geq \tau)-(p \mathbb{E}(\tilde{x}|\tilde{x}\geq \tau))^{2} \\ &=& p(Var(\tilde{x}|\tilde{x}\geq \tau)+ \mathbb{E}(\tilde{x}|\tilde{x}\geq \tau)^{2})-(p \mathbb{E}(\tilde{x}|\tilde{x}\geq \tau))^{2}\\ &=& p(Var(\tilde{x}|\tilde{x}\geq \tau)+ (\mathbb{E}(\tilde{x}|\tilde{x}\geq \tau))^{2} (1-p))=p(v_{x}+(1-p)m^{2}). \end{array} $$

Next, note that \(\hat {c}_{NP}=G(\hat {p},\hat {w})\) where \(G(X)=\hat {\tau }+\frac {z}{1-y}\) and X = (y,z). Hence, applying the delta method,

$$ \sqrt{N}(\hat{c}_{NP}^{}-c^{})\rightarrow_{d} N(0,\underbrace{A V_{0} A^{\prime}}_{\sigma_{NP}^{2}}) $$

such that \(A=\frac {\partial G}{\partial X^{\prime }}|_{X=(p,pm)}=(\frac {pm}{(1-p)^{2}}, \frac {1}{1-p})\). Therefore,

$$ \begin{array}{@{}rcl@{}} \sigma_{NP}^{2}&=&(\frac{pm}{(1-p)^{2}}, \frac{1}{1-p})\left( \begin{array}{ll} p(1-p) & (1-p)p m \\ (1-p)p m & p(v_{x}+(1-p)m^{2}) \end{array}\right) \left( \begin{array}{l} \frac{pm}{(1-p)^{2}} \\ \frac{1}{1-p} \end{array}\right)\\ &=& \frac {p (p m + m (1 - p))^{2} + (1 - p) p v_{x}} {(1 - p)^{3}}. \end{array} $$

To complete the proof, we further show that \(\hat {\tau }\) converges at a rate greater than \(\sqrt {N}\). We define J(.), the distribution of x|x > τ and let t > 0, b ∈ (0,p) and α ∈ (1/2, 1). Letting m be the number of disclosures, we can decompose the probability \(Prob(N^{\alpha }(\hat {\tau }-\tau )\leq t)\) as follows:

$$ \begin{array}{@{}rcl@{}} \forall t>0,Prob(N^{\alpha}(\hat{\tau}-\tau)\leq t)=Prob(m< bN)Prob(N^{\alpha}(\hat{\tau}-\tau)\leq t|m<bN)\\ +Prob(m> b N)Prob(N^{\alpha}(\hat{\tau}-\tau)\leq t|m>bN+1),\\ \geq Prob(N^{\alpha}(\hat{\tau}-\tau)\leq t|m>[bN])+o(1/N), \end{array} $$

where the inequality follows from the fact that Prob(m < bN) converges to zero as N becomes large and \(Prob(N^{\alpha }(\hat {\tau }-\tau )\leq t|m)\) is decreasing in m. The probability in the right-hand side is, up to a negligible term, equal to

$$ \begin{array}{@{}rcl@{}} 1-\left( 1-J\left( \frac{t}{N^{\alpha}}+\tau\right)\right)^{bN} &=&1-\exp \left( bN log\left( 1-J\left( \frac{t}{N^{\alpha}}+\tau\right)\right)\right). \end{array} $$

Taking the limit in \(N\rightarrow +\infty ,\)

$$ \begin{array}{@{}rcl@{}} lim_{N\rightarrow+\infty}\frac{ log(1-J(\frac{t}{N^{\alpha}}+\tau))}{\frac{t}{N^{\alpha}}}=-\frac{J^{\prime}(\tau)}{1-J(\tau)}=-J^{\prime}(\tau)<0. \end{array} $$

Hence \(lim_{N\rightarrow +\infty }1-\exp (bN log(1-J(\frac {t}{N^{\alpha }}+\tau )))= {lim_{N}\rightarrow +\infty }1-\exp (bNt \frac { log(1-J(\frac {t}{N^{\alpha }}+\tau ))}{\frac {t}{N^{\alpha }}})=1\). We conclude: \(lim_{N\rightarrow +\infty }Prob(N^{\alpha }(\hat {\tau }-\tau )\leq t)=1\). □

Appendix: B

We prove next that the NP estimator derived under pure disclosure costs continues to hold, even if there is an uncertain information endowment coupled with an inability to credibly communicate a lack of information, as in Dye (1985), or a probability that managers do not care about market perceptions, which would induce them to never engage in costly disclosure.

In addition to a disclosure cost c, the manager may not be informed with some probability q > 0 and then cannot disclose. Although this theoretical assumption is not parsimonious, the reader may note that we are trying to take frictions that may simultaneously exist in the data (Einhorn and Ziv 2008) and hence speak to the fair concern that what we identify as a disclosure cost may, in fact, be uncertain information endowment. In this joint model, the equation for the disclosure threshold remains

$$ \tau-c=\mathbb{E}(x|ND), $$

where the right-hand side is the expected value conditional on not disclosing and is now a function of p as in Jung and Kwon (1988).Footnote 27

Even though the non-disclosure expectation will be different in this model, we can denote p = (1 − q)(1 − F(τ)), i.e., the probability to disclose, where F(.) is the cumulative probability density of x, and apply the law of total expectations as in the baseline:

$$ \begin{array}{@{}rcl@{}} 0=\mathbb{E}(x)=p\mathbb{E}(x|x\geq\tau)+(1-p)\mathbb{E}(x|ND). \end{array} $$

Solving for E(x|ND) and plugging this equation into (B) implies the same estimator as NP,

$$ c=\tau+\frac{p}{1-p}\mathbb{E}(x|x\geq \tau)). $$

Hence the NP estimator derived under pure disclosure costs continues to hold even if there is uncertainty about information endowment although (as we have shown) this other friction affects the disclosure threshold. The key to this finding is that the probability of disclosure p is endogenous and changes as q increases; we only need to observe this endogenous variable to recover the cost c.

Appendix C: Variable definitions

Table 9

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Cheynel, E., Liu-Watts, M. A simple structural estimator of disclosure costs. Rev Account Stud 25, 201–245 (2020).

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  • Voluntary disclosures
  • Disclosure costs
  • Proprietary costs
  • Structural estimation
  • Management forecasts

JEL Classification

  • C14
  • D21
  • D22
  • D83
  • G14
  • M4